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At least 19 recordsLinked to original sources

The effect of functional response on stability of a grazer population on a landscape

The dynamics of interacting consumer and resource populations is one of the most thoroughly studied problems of theoretical population biology. Among the key results from the study of simple mathematical models of interacting populations is that the Holling Type 2 functional response tends to be unstable for a wide range of realistic parameters. Functional responses such as Holling Type 3, which might be thought of as implicitly incorporating the existence of consumer refuges, are more stable than the Type 2. We studied consumer—resource models with these different functional responses on a landscape level by modeling grazers that can disperse across a space of patchily distributed grass resources. For certain assumptions concerning the movement of grazers on the landscape, the effect of these functional responses on stability is reversed; the Holling Type 2 functional response confers greater stability. The reason for this apparently paradoxical result is that the Holling Type 2 functional response allows grazers to graze individual grass patches to lower levels than Type 3, as the energy balance remains favorable for grazing at lower grass biomasses. However, this local overexploitation leads the grazers to be slower in reaching areas of the landscape where resource densities are higher. It decreases the likelihood that the resource will be overexploited over the whole landscape simultaneously, which results in a stronger tendency towards system stability. It appears, then, that consumer overexploitation of resources locally may contribute to lower stability.

Ecological Modelling↗

Source-sink dynamics and the coexistence of species on a single resource

We investigate the potential for coexistence of species that compete for a shared resource when the resource occurs in both a source area acting as a refuge and a sink area where it is used by the competing species. Our model shows that the mixing rate between the source and sink resource populations has a dramatic influence on the outcome of competition. When there is a strict sink–source dependence, so that resource renewal in the sink is entirely dependent on the source, only exploitation competition decides which species can survive at a very small mixing rate. Increasing the flow rate basically amounts to increasing the role played by interference competition. If interspecific interference is very small, compared with intraspecific interference, increasing the mixing rate allows coexistence of many species, indeed, unlimited coexistence if the species' resource exploitation efficiencies are similar enough. If interspecific interference is significant and there is a trade-off between the exploitation and interference competitive abilities of two species, it is possible to have one species replacing the other along a gradient of increasing mixing rate, with either coexistence or alternative single-species equilibria at intermediate values of the mixing rate. It is also possible to have one species always outcompeting the other, or alternative single-species stable equilibria at large mixing rates. When the strict sink–source dependence is relaxed by allowing the resource to have a partly independent renewal–loss dynamics in the sink area, the variety of possible outcomes along a gradient of mixing rate is further increased. These outcomes are often strongly sensitive to the parameters of resource dynamics and interspecific interference competition. The implications of these results for biological conservation can be profound; detailed knowledge of interspecific interactions appears to be necessary to determine the effect of any land management that alters dispersal opportunities.

Theoretical Population Biology↗

Effects of spatial grouping on the functional response of predators

A unified mechanistic approach is given for the derivation of various forms of functional response in predator-prey models. The derivation is based on the principle-of-mass action but with the crucial refinement that the nature of the spatial distribution of predators and/or opportunities for predation are taken into account in an implicit way. If the predators are assumed to have a homogeneous spatial distribution, then the derived functional response is prey-dependent. If the predators are assumed to form a dense colony or school in a single (possibly moving) location, or if the region where predators can encounter prey is assumed to be of limited size, then the functional response depends on both predator and prey densities in a manner that reflects feeding interference between predators. Depending on the specific assumptions, the resulting functional response may be of Beddington-DeAngelis type, of Hassell-Varley type, or ratio-dependent.

Theoretical Population Biology↗

Structural instability, multiple stable states, and hysteresis in periphyton driven by phosphorus enrichment in the Everglades

Periphyton is a key component of the Everglades ecosystems. It is a major primary producer, providing food and habitat for a variety of organisms, contributing material to the surface soil, and regulating water chemistry. Periphyton is sensitive to the phosphorus (P) supply and P enrichment has caused dramatic changes in the native Everglades periphyton assemblages. Periphyton also affects P availability by removing P from the water column and depositing a refractory portion into sediment. A quantitative understanding of the response of periphyton assemblages to P supply and its effects on P cycling could provide critical supports to decision making in the conservation and restoration of the Everglades. We constructed a model to examine the interaction between periphyton and P dynamics. The model contains two differential equations: P uptake and periphyton growth are assumed to follow the Monod equation and are limited by a modified logistic equation. Equilibrium and stability analyses suggest that P loading is the driving force and determines the system behavior. The position and number of steady states and the stability also depend upon the rate of sloughing, through which periphyton deposits refractory P into sediment. Multiple equilibria may exist, with two stable equilibria separated by an unstable equilibrium. Due to nonlinear interplay of periphyton and P in this model, catastrophe and hysteresis are likely to occur.

Florida↗

Ecological and evolutionary conditions for fruit abortion to regulate pollinating seed-eaters and increase plant production

Coevolved mutualisms, such as those between senita cacti, yuccas, and their respective obligate pollinators, benefit both species involved in the interaction. However, in these pollination mutualisms the pollinator's larvae impose a cost on plants through consumption of developing seeds and fruit. The effects of pollinators on benefits and costs are expected to vary with the abundance of pollinators, because large population sizes result in more eggs and larval seed-eaters. Here, we develop the hypothesis that fruit abortion, which is common in yucca, senita, and plants in general, could in some cases have the function of limiting pollinator abundance and, thereby, increasing fruit production. Using a general steady-state model of fruit production and pollinator dynamics, we demonstrate that plants involved in pollinating seed-eater mutualisms can increase their fecundity by randomly aborting fruit. We show that the ecological conditions under which fruit abortion can improve plants fecundity are not unusual. They are best met when the plant is long-lived, the population dynamics of the pollinator are much faster than those of the plant, the loss of one fruit via abortion kills a larva that would have the expectation of destroying more than one fruit through its future egg laying as an adult moth, and the effects of fruit abortion on pollinator abundance are spatially localized. We then use the approach of adaptive dynamics to find conditions under which a fruit abortion strategy based on regulating the pollinator population could feasibly evolve in this type of plant–pollinator interaction.

Theoretical Population Biology↗

The effects of mixotrophy on the stability and dynamics of a simple planktonic food web

Recognition of the microbial loop as an important part of aquatic ecosystems disrupted the notion of simple linear food chains. However, current research suggests that even the microbial loop paradigm is a gross simplification of microbial interactions due to the presence of mixotrophs—organisms that both photosynthesize and graze. We present a simple food web model with four trophic species, three of them arranged in a food chain (nutrients–autotrophs–herbivores) and the fourth as a mixotroph with links to both the nutrients and the autotrophs. This model is used to study the general implications of inclusion of the mixotrophic link in microbial food webs and the specific predictions for a parameterization that describes open ocean mixed layer plankton dynamics. The analysis indicates that the system parameters reside in a region of the parameter space where the dynamics converge to a stable equilibrium rather than displaying periodic or chaotic solutions. However, convergence requires weeks to months, suggesting that the system would never reach equilibrium in the ocean due to alteration of the physical forcing regime. Most importantly, the mixotrophic grazing link seems to stabilize the system in this region of the parameter space, particularly when nutrient recycling feedback loops are included.

Theoretical Population Biology↗

Assessing spatial coupling in complex population dynamics using mutual prediction and continuity statistics

A number of important questions in ecology involve the possibility of interactions or ?coupling? among potential components of ecological systems. The basic question of whether two components are coupled (exhibit dynamical interdependence) is relevant to investigations of movement of animals over space, population regulation, food webs and trophic interactions, and is also useful in the design of monitoring programs. For example, in spatially extended systems, coupling among populations in different locations implies the existence of redundant information in the system and the possibility of exploiting this redundancy in the development of spatial sampling designs. One approach to the identification of coupling involves study of the purported mechanisms linking system components. Another approach is based on time series of two potential components of the same system and, in previous ecological work, has relied on linear cross-correlation analysis. Here we present two different attractor-based approaches, continuity and mutual prediction, for determining the degree to which two population time series (e.g., at different spatial locations) are coupled. Both approaches are demonstrated on a one-dimensional predator?prey model system exhibiting complex dynamics. Of particular interest is the spatial asymmetry introduced into the model as linearly declining resource for the prey over the domain of the spatial coordinate. Results from these approaches are then compared to the more standard cross-correlation analysis. In contrast to cross-correlation, both continuity and mutual prediction are clearly able to discern the asymmetry in the flow of information through this system.

Theoretical Population Biology↗

Establishing a beachhead: A stochastic population model with an Allee effect applied to species invasion

We formulated a spatially explicit stochastic population model with an Allee effect in order to explore how invasive species may become established. In our model, we varied the degree of migration between local populations and used an Allee effect with variable birth and death rates. Because of the stochastic component, population sizes below the Allee effect threshold may still have a positive probability for successful invasion. The larger the network of populations, the greater the probability of an invasion occurring when initial population sizes are close to or above the Allee threshold. Furthermore, if migration rates are low, one or more than one patch may be successfully invaded, while if migration rates are high all patches are invaded. ?? 2007 Elsevier Inc. All rights reserved.

Theoretical Population Biology↗

Plant-herbivore interactions mediated by plant toxicity

We explore the impact of plant toxicity on the dynamics of a plant-herbivore interaction, such as that of a mammalian browser and its plant forage species, by studying a mathematical model that includes a toxin-determined functional response. In this functional response, the traditional Holling Type 2 response is modified to include the negative effect of toxin on herbivore growth, which can overwhelm the positive effect of biomass ingestion at sufficiently high plant toxicant concentrations. Two types of consumption decisions of the herbivore are considered. One of these (Case 1) incorporates the adaptation of the herbivore to control its rate of consumption of plant items when that is likely to lead to levels of toxicity that more than offset the marginal gain to the herbivore of consuming more plant biomass, while the other (Case 2) simply assumes that, although the herbivore's rate of ingestion of plant biomass is negatively affected by increasing ingestion of toxicant relative to the load it can safely deal with, the herbivore is not able to prevent detrimental or even lethal levels of toxicant intake. A primary result of this work is that these differences in behavior lead to dramatically different outcomes, summarized in bifurcation diagrams. In Case 2, a wide variety of dynamics may occur due to the interplay of Holling Type 2 dynamics and the effect of the plant toxicant. These dynamics include the occurrence of bistability, in which both a periodic solution and the herbivore-extinction equilibrium are attractors, as well the possibility of a homoclinic bifurcation. Whether the herbivore goes to extinction in the bistable case depends on initial conditions of herbivore and plant biomasses. For relatively low herbivore resource acquisition rates, the toxicant effect increases the likelihood of 'paradox of enrichment' type limit cycle oscillations, but at higher resource acquisition rates, the toxicant may decrease the likelihood of these cycles. ?? 2007 Elsevier Ltd. All rights reserved.

Theoretical Population Biology↗

Host mating system and the spread of a disease-resistant allele in a population

The model presented here modifies a susceptible-infected (SI) host-pathogen model to determine the influence of mating system on the outcome of a host-pathogen interaction. Both deterministic and stochastic (individual-based) versions of the model were used. This model considers the potential consequences of varying mating systems on the rate of spread of both the pathogen and resistance alleles within the population. We assumed that a single allele for disease resistance was sufficient to confer complete resistance in an individual, and that both homozygote and heterozygote resistant individuals had the same mean birth and death rates. When disease invaded a population with only an initial small fraction of resistant genes, inbreeding (selfing) tended to increase the probability that the disease would soon be eliminated from a small population rather than become endemic, while outcrossing greatly increased the probability that the population would become extinct due to the disease.

Theoretical Population Biology↗

Towards a theory of ecotone resilience: coastal vegetation on a salinity gradient

Ecotones represent locations where vegetation change is likely to occur as a result of climate and other environmental changes. Using a model of an ecotone vulnerable to such future changes, we estimated the resilience of the ecotone to disturbances. The specific ecotone is that between two different vegetation types, salinity-tolerant and salinity-intolerant, along a gradient in groundwater salinity. In the case studied, each vegetation type, through soil feedback loops, promoted local soil salinity levels that favor itself in competition with the other type. Bifurcation analysis was used to study the system of equations for the two vegetation types and soil salinity. Alternative stable equilibria, one for salinity-tolerant and one for salinity intolerant vegetation, were shown to exist over a region of the groundwater salinity gradient, bounded by two bifurcation points. This region was shown to depend sensitively on parameters such as the rate of upward infiltration of salinity from groundwater into the soil due to evaporation. We showed also that increasing diffusion rates of vegetation can lead to shrinkage of the range between the two bifurcation points. Sharp ecotones are typical of salt-tolerant vegetation (mangroves) near the coastline and salt-intolerant vegetation inland, even though the underlying elevation and groundwater salinity change very gradually. A disturbance such as an input of salinity to the soil from a storm surge could upset this stable boundary, leading to a regime shift of salinity-tolerant vegetation inland. We showed, however, that, for our model as least, a simple pulse disturbance would not be sufficient; the salinity would have to be held at a high level, as a 'press', for some time. The approach used here should be generalizable to study the resilience of a variety of ecotones to disturbances.

Theoretical Population Biology↗

Energetic constraints and the paradox of a diffusing population in a heterogeneous environment

Previous mathematical analyses have shown that, for certain parameter ranges, a population, described by logistic equations on a set of connected patches, and diffusing among them, can reach a higher equilibrium total population when the local carrying capacities are heterogeneously distributed across patches, than when carrying capacities having the same total sum are homogeneously distributed across the patches. It is shown here that this apparently paradoxical result is explained when the resultant differences in energy inputs to the whole multi-patch system are taken into account. We examine both Pearl–Verhulst and Original Verhulst logistic models and show that, when total input of energy or limiting resource, is constrained to be the same in the homogeneous and heterogeneous cases, the total population in the heterogeneous patches can never reach an asymptotic equilibrium that is greater than the sum of the carrying capacities over the homogeneous patches. We further show that, when the dynamics of the limiting resources are explicitly modeled, as in a chemostat model, the paradoxical result of the logistic models does not occur. These results have implications concerning the use of some ubiquitous equations of population ecology in modeling populations in space.

Theoretical Population Biology↗

Dispersal asymmetry in a two-patch system with source–sink populations

This paper analyzes source–sink systems with asymmetric dispersal between two patches. Complete analysis on the models demonstrates a mechanism by which the dispersal asymmetry can lead to either an increased total size of the species population in two patches, a decreased total size with persistence in the patches, or even extinction in both patches. For a large growth rate of the species in the source and a fixed dispersal intensity, (i) if the asymmetry is small, the population would persist in both patches and reach a density higher than that without dispersal, in which the population approaches its maximal density at an appropriate asymmetry; (ii) if the asymmetry is intermediate, the population persists in both patches but reaches a density less than that without dispersal; (iii) if the asymmetry is large, the population goes to extinction in both patches; (iv) asymmetric dispersal is more favorable than symmetric dispersal under certain conditions. For a fixed asymmetry, similar phenomena occur when the dispersal intensity varies, while a thorough analysis is given for the low growth rate of the species in the source. Implications for populations in heterogeneous landscapes are discussed, and numerical simulations confirm and extend our results.

Theoretical Population Biology↗

Variability in population abundance is associated with thresholds between scaling regimes

Discontinuous structure in landscapes may result in discontinuous, aggregated species body-mass patterns, reflecting the scales of structure available to animal communities within a landscape. The edges of these body-mass aggregations reflect transitions between available scales of landscape structure. Such transitions, or scale breaks, are theoretically associated with increased biological variability. We hypothesized that variability in population abundance is greater in animal species near the edge of body-mass aggregations than it is in species that are situated in the interior of body-mass aggregations. We tested this hypothesis by examining both temporal and spatial variability in the abundance of species in the bird community of the Florida Everglades sub-ecoregion, USA. Analyses of both temporal and spatial variability in population abundance supported our hypothesis. Our results indicate that variability within complex systems may be non-random, and is heightened where transitions in scales of process and structure occur. This is the first explicit test of the hypothetical relationship between increased population variability and scale breaks. ?? 2009 by the author(s).

Ecology and Society↗

Statistical inference from capture data on closed animal populations

The estimation of animal abundance is an important problem in both the theoretical and applied biological sciences. Serious work to develop estimation methods began during the 1950s, with a few attempts before that time. The literature on estimation methods has increased tremendously during the past 25 years (Cormack 1968, Seber 1973). However, in large part, the problem remains unsolved. Past efforts toward comprehensive and systematic estimation of density (D) or population size (N) have been inadequate, in general. While more than 200 papers have been published on the subject, one is generally left without a unified approach to the estimation of abundance of an animal population This situation is unfortunate because a number of pressing research problems require such information. In addition, a wide array of environmental assessment studies and biological inventory programs require the estimation of animal abundance. These needs have been further emphasized by the requirement for the preparation of Environmental Impact Statements imposed by the National Environmental Protection Act in 1970. This publication treats inference procedures for certain types of capture data on closed animal populations. This includes multiple capture-recapture studies (variously called capture-mark-recapture, mark-recapture, or tag-recapture studies) involving livetrapping techniques and removal studies involving kill traps or at least temporary removal of captured individuals during the study. Animals do not necessarily need to be physically trapped; visual sightings of marked animals and electrofishing studies also produce data suitable for the methods described in this monograph. To provide a frame of reference for what follows, we give an exampled of a capture-recapture experiment to estimate population size of small animals using live traps. The general field experiment is similar for all capture-recapture studies (a removal study is, of course, slightly different). A typical field experiment is the following: a number of traps are positioned in the area to be studied, say 144 traps in a 12 X 12 grid, 7 m apart. At the beginning of the study (j=1) a sample size of n 1 is taken from the population, the animals are tagged and marked for future identification, and then returned to the population, usually at the same point where they were trapped. After allowing time of the marked and unmarked animals to mix, a second sample (j=2, often the following day) or n 2 animals is then taken.the second sample normally contains both marked and unmarked animals. The unmarked animals are marked and all captured animals are released back into the population. This procedure continues for t periods where t ≥ 2. The animals should be marked in such a way that the capture-recapture history of each animal caught during the study is known. In practice, toes are often clipped to uniquely identify individual animals (Taber and Cowan 1969) or serially numbered tags are sometimes used on larger animals. Such capture studies are classified by 2 schemes that are directly related to what class of models are appropriate and what parameters can be estimated. The first classification addresses the subject of closure. Closure usually means the size of the population is constant over the priod of investigation, i.e., no recruitment (birth or immigration) or losses (death or emigration). This is a strong assumption and, of course, never completely true in a natural biological population. For greater generality, we define closure to mean there are no unknown changes to the initial population. In practice, this means known losses (trap death), or deliberate removals) do not violate our definition of closure. If the study is properly designed, closure can be met at least approximately. Open or nonclosed populations explicitly allow for one or more types of recruitment or losses to operate during the course of the experiment (Jolly 1965, Seber 1965, Robson 1969, Pollock 1975). Only closed populations will be considered in this monograph. The second classification depends on the type of data collected with 2 possibilities occurring (Pollock 1974, unpublished doctoral dissertation, Cornell University, Ithaca, New York): (1) only information on the recovery of marked animals is available for each sampling occasion, j, j=1, 2, ... t. (2) information on both marked and unmarked animals is available for each sampling occasion, j, j=1, 2, ... t. In case (1), population size (N) is not identifiable, however, other parameters can be estimated (Brownie et al. 1978). In case (2), N can be estimated using a wide variety of approaches depending upon what we wish to assume. Only case (2) will be dealt with here.

Wildlife Monographs↗

Negative binomial models for abundance estimation of multiple closed populations

Counts of uniquely identified individuals in a population offer opportunities to estimate abundance. However, for various reasons such counts may be burdened by heterogeneity in the probability of being detected. Theoretical arguments and empirical evidence demonstrate that the negative binomial distribution (NBD) is a useful characterization for counts from biological populations with heterogeneity. We propose a method that focuses on estimating multiple populations by simultaneously using a suite of models derived from the NBD. We used this approach to estimate the number of female grizzly bears (Ursus arctos) with cubs-of-the-year in the Yellowstone ecosystem, for each year, 1986-1998. Akaike's Information Criteria (AIC) indicated that a negative binomial model with a constant level of heterogeneity across all years was best for characterizing the sighting frequencies of female grizzly bears. A lack-of-fit test indicated the model adequately described the collected data. Bootstrap techniques were used to estimate standard errors and 95% confidence intervals. We provide a Monte Carlo technique, which confirms that the Yellowstone ecosystem grizzly bear population increased during the period 1986-1998.

Idaho, Montana, Wyoming↗

Design and implementation of estimation-based monitoring programs for flora and fauna: A case study on the Cherokee National Forest

Science-based monitoring of biological resources is important for a greater understanding of ecological systems and for assessment of the target population using theoretic-based management approaches. When selecting variables to monitor, managers first need to carefully consider their objectives, the geographic and temporal scale at which they will operate, and the effort needed to implement the program. Generally, monitoring can be divided into two categories: index and inferential. Although index monitoring is usually easier to implement, analysis of index data requires strong assumptions about consistency in detection rates over time and space, and parameters are often biasednot accounting for detectability and spatial variation. In most cases, individuals are not always available for detection during sampling periods, and the entire area of interest cannot be sampled. Conversely, inferential monitoring is more rigorous because it is based on nearly unbiased estimators of spatial distribution. Thus, we recommend that detectability and spatial variation be considered for all monitoring programs that intend to make inferences about the target population or the area of interest. Application of these techniques is especially important for the monitoring of Threatened and Endangered (T&E) species because it is critical to determine if population size is increasing or decreasing with some level of certainty. Use of estimation-based methods and probability sampling will reduce many of the biases inherently associated with index data and provide meaningful information with respect to changes that occur in target populations. We incorporated inferential monitoring into protocols for T&E species spanning a wide range of taxa on the Cherokee National Forest in the Southern Appalachian Mountains. We review the various approaches employed for different taxa and discuss design issues, sampling strategies, data analysis, and the details of estimating detectability using site occupancy. These techniques provide a science-based approach for monitoring and can be of value to all resource managers responsible for management of T&E species.

Proceedings of the Annual Conference of the Southe↗

Effects of diffusion on total biomass in heterogeneous continuous and discrete-patch systems

Theoretical models of populations on a system of two connected patches previously have shown that when the two patches differ in maximum growth rate and carrying capacity, and in the limit of high diffusion, conditions exist for which the total population size at equilibrium exceeds that of the ideal free distribution, which predicts that the total population would equal the total carrying capacity of the two patches. However, this result has only been shown for the Pearl-Verhulst growth function on two patches and for a single-parameter growth function in continuous space. Here, we provide a general criterion for total population size to exceed total carrying capacity for three commonly used population growth rates for both heterogeneous continuous and multi-patch heterogeneous landscapes with high population diffusion. We show that a sufficient condition for this situation is that there is a convex positive relationship between the maximum growth rate and the parameter that, by itself or together with the maximum growth rate, determines the carrying capacity, as both vary across a spatial region. This relationship occurs in some biological populations, though not in others, so the result has ecological implications.

Theoretical Ecology↗